Barack Obama has told crucial UN climate talks in Paris that the negotiations represent an “act of defiance” after the barbaric attacks in the city two weeks ago in which 130 people were killed.

Offering his condolences and pledging solidarity with the people of “this beautiful city” he said, “We have come to Paris to show our resolve ... to protect our people, and to uphold the enduring values that keep us strong and keep us free. We salute the people of Paris for insisting this crucial conference go on.”

Current international commitments on curbing emissions, from developed and developing countries, run out in 2020, and the following decade will be crucial in deciding whether dangerous climate change takes hold, as infrastructure like power stations and transport links built in the next 15 years will still be used for half a century to come. If it is not built to low-carbon standards, and current emissions are not curbed, the world is in danger of temperature rises of up to 5C – levels that would cause dramatic changes in weather and ravage huge swathes of the globe.

Obama said that the attendance of world leaders was a “rejection of those who would tear down our world”, and drew parallels between the ravages of climate change and terrorism. “[We want] a declaration that, for all the challenges we face, climate change could define the contours of this century more dramatically than any other.”

He warned of some of the likely effects of climate change: “Submerged countries; abandoned cities; fields that no longer grow; political disruptions that trigger new conflict; and even more floods of desperate peoples seeking sanctuary in nations not their own.”

The Paris conference could change that, he said: “This future is one that we have the power to change – right here, right now.”

“One of the enemies we will be fighting at this conference is cynicism – the notion that we can’t do anything about climate change,” he added.

Poor nations must receive particular help, he urged. “We must reaffirm our commitment that the resources will be there [in financial assistance for the developing world]. We must make sure these resources [of climate finance] fall to countries that need help … and help vulnerable populations rebuild stronger after climate related disasters.”

A cause for hope, he said, was that a sense of urgency was growing among nations, as well as an increasing realisation that it is within our power to tackle climate change.

Obama said the US embraced its responsibility – as the world’s largest economy and second largest emitter – to act, and called for unity among world leaders attending the talks. He urged a “common purpose [for a] world that is not marked not by conflict but by cooperation – not by human suffering but human progress.”

However, although world leaders were anxious to stress their solidarity with Paris and their support for the UN negotiations, tensions were also clearly visible. Vladimir Putin of Russia and Obama barely made eye contact on meeting, and in a private meeting with Obama, the Indian president Narendra Modi is understood to have made it clear he thinks developed countries should take on substantial carbon cuts while allowing poor nations to increase their emissions.

While pledging India to protect the planet, and announcing new initiatives on solar power, Modi was adamant: “Climate change is not of our making. It is the result of global warming that came from an industrial age powered by fossil fuel.”

Speaking shortly after Obama, China’s president Xi Jinping said the eyes of the world were on Paris and that, “tackling climate change is a shared mission for all mankind.” He reiterated the country’s pledge to peak its emissions by 2030 and said: “we have confidence and resolve to fulfil our commitments”.

Pointedly, he also insisted that developing countries must not be prevented from growing their economies by having to deal with emissions and the impacts of warming: “Addressing climate change should not deny the legitimate needs of developing countries to reduce poverty.”

A crucial issue at the talks will be how to provide financial assistance to the poorest countries, to help them cut their emissions and deal with the effects of climate change. Another will be a long-term pledge not to let global temperatures rise beyond the widely agreed danger threshold of 2C, beyond which scientists say climate change will become catastrophic and irreversible. But a number of poor nations, endorsed by the UN’s climate chief, have made it clear they want a lower limit, of 1.5C, to protect small islands from swamping and the poorest nations from extreme weather. That debate has been left open by the French presidency.

Ban Ki-moon, UN secretary general, urged countries to come to a deal: ”Please, let’s meet on the middle ground, show some flexibility and sense of compromise for the common good. We can’t go on like this. We can’t waste any further time.”

Laurent Fabius, the French foreign minister who is hosting the talks as COP president, said: “COP21 needs to be a tipping point, a turning point. The Paris conference will no doubt not resolve everything, but nothing can be resolved without it. It is France’s responsibility to help address two of the greatest challenges of the century: combating terrorism and fighting climate change. Today’s generations are calling upon us to act, while tomorrow’s generations will judge our action. We cannot hear them yet, but in a way they are already watching us.”

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David Cameron, the UK prime minister, also urged action. He stood alongside Prince Charles for the opening ceremony, as all of the leaders posed for a “family” photograph.

Leaders spent most of the day making speeches, leaving their supporting teams anxious in some cases that the timetable for private meetings – the core reason for the leaders’ presence, to iron out remaining differences and create an atmosphere of diplomatic cooperation in which a deal can be brokered – would be squeezed. However, many expected to work long into the night, while negotiators carried on their meetings on a draft text of an agreement behind closed doors.